(4k²+2k+1)+(-4k²+2k-1)

To add the given expressions, we can simply combine like terms.

(4k² + 2k + 1) + (-4k² + 2k - 1)

Combine the terms with the same variable: (4k² - 4k²) + (2k + 2k) + (1 - 1)

The terms with the same variable and exponent cancel each other out, and the terms without variables can be simplified:

0 + 4k + 0

Therefore, the result is 4k.